Решите уравнения 1. log2 (10x) - log2 (4x+156) = log2 1-7log7 4

2. log15 (6-35x) * log44 (1-2x) = log8 1

3. log2 (x+1) + log2 (4x+4) = 6

решите уравнения

1. log2 (10x) - log2 (4x+156) = log2 1-7log7 4

log2 (10x / (4x+156)) = 0-7[log2 4]/log2 7

все верно в условии?

2. log15 (6-35x) * log44 (1-2x) = log8 1

log15 (6-35x) * log44 (1-2x) = 0 ⇔

1) log15 (6-35x) = 0 2) log44 (1-2x) = 0

(6-35x) = 1 x=1/7 1-2x=1 x=0

проверка

log15 (1) * log44 (1-2/7) = 0 верно log15 (6-0) * log44 (1) = 0 верно

3. log2 (x+1) + log2 (4x+4) = 6 одз: x+1>0⇔x>-1

(x+1) (4x+4) = 2^6

4 (x+1) ²=4·2^4

(x+1) ²=4²

(x+1-4) (x+1+4) = 0 x=3 x=-5∉ одз: x>-1